Put the grated courgettes in a colander and sprinkle with 1 tsp of the salt. Leave to stand for 20 mins, then, using your hands, squeeze out as much of the moisture as possible. Rinse the courgettes thoroughly, then squeeze again.
Heat 1 tbsp of the olive oil in a frying pan and cook the onion and garlic for 4 mins until softened. Add the mushrooms and cook for a further 4 mins until softened and browned, then add the courgettes and cook for another 2 mins. Strain well and set aside to cool; discard the liquid.
Heat oven to 220C/fan 200C/gas 7. Place the flour in a large mixing bowl, stir in the yeast, the remaining oil and salt, the basil and the courgette mixture. Mix well to combine. Make a well in the centre and add 125ml hand-hot water. Mix well to form a slightly sticky dough. Knead on a floured surface for about 10 mins, then shape into a ball and place on a greased baking sheet.
Flatten the ball of dough very slightly with the palm of your hand and loosely cover with oiled cling film. Leave to rise in a warm place for 25-30 mins until doubled in size. Brush the top of the dough with a little water, then sprinkle with the sea salt and bake for 40 mins until golden. Leave to cool on a wire rack before serving.